We present a computational study of spontaneous polarization and piezoelectricity in Sc _x Al _{1− x} N alloys in the compositional range from x = 0 to x = 0.5, obtained in the context of density functional theory and the Berry-phase theory of electric polarization using large periodic supercells. We report composition-dependent values of piezoelectric coefficients e _ij , piezoelectric moduli d _ij and elastic constants C _ij . The theoretical findings are complemented with experimental measurement of e ₃₃ for a series of sputtered ScAlN films carried out with a piezoelectric resonator. The rapid increase with Sc content of the piezoelectric response reported in previous studies is confirmed for the available data. A detailed description of the full methodology required to calculate the piezoelectric properties of ScAlN, with application to other complex alloys, is presented. In particular, we find that the large amount of internal strain present in ScAlN and its intricate relation with electric polarization make configurational sampling and the use of large supercells at different compositions necessary in order to accurately derive the piezoelectric response of the material.

We study the deposition of tetrahedral amorphous carbon (ta-C) films from molecular dynamics simulations based on a machine-learned interatomic potential trained from density-functional theory data. For the first time, the high $s{p}^3$ fractions in excess of 85% observed experimentally are reproduced by means of computational simulation, and the deposition energy dependence of the film’s characteristics is also accurately described. High confidence in the potential and direct access to the atomic interactions allow us to infer the microscopic growth mechanism in this material. While the widespread view is that ta-C grows by “subplantation,” we show that the so-called “peening” model is actually the dominant mechanism responsible for the high $s{p}^3$ content. We show that pressure waves lead to bond rearrangement away from the impact site of the incident ion, and high $s{p}^3$ fractions arise from a delicate balance of transitions between three- and fourfold coordinated carbon atoms. These results open the door for a microscopic understanding of carbon nanostructure formation with an unprecedented level of predictive power.